ME102: Mechanics I

Unit 2: Material Mechanics and Analysis of Solid Objects
*In this unit,we will examine the effects that forces have on
solids. You will understand how forces produce stress and strain and
deform bodies, as well as how bodies behave in elastic and plastic
regions. You will study stress developed in bodies due to linear forces
and moments in pure tension or compression, bending, and torsion. We
will take a look at centroids, centers of mass, and moments of
inertia—structure-specific properties that are related to mass and that
help us define how an object will react to an applied force. We will
begin with the simplest objects in order to help you best understand new
concepts, such as stress and strain, more easily. In its most basic
terms, stress is defined as the amount of internal force acting on an
object, per unit area. Strain, on the other hand, is used to describe
the deformation of an object, or the change in the object’s shape as the
result of loading. More specifically, it describes the structure’s
elongation. For example, imagine putting an orange into a vice and
tightening it. The soft fruit will compress, because there is a lot of
stress acting upon it. It will also change shape; strain often occurs
in the presence of stress. *

Unit 2 Time Advisory
This unit will take you approximately 36.5 hours to complete.

☐ Subunit 2.1: 2.5 hours

☐ Subunit 2.1.1: 1.5 hours

☐ Subunit 2.1.2: 1 hour
☐ Subunit 2.2: 10.5 hours

☐ Subunit 2.2.1: 3 hours

☐ Subunit 2.2.2: 2 hours

☐ Subunit 2.2.3: 3 hours

☐ Subunit 2.2.4: 2 hours

☐ Subunit 2.2.5: 0.5 hours

☐ Subunit 2.3: 11.5 hours

☐ Subunit 2.3.1: 2 hours

☐ Subunit 2.3.2: 3 hours

☐ Subunit 2.3.3: 2.5 hours

☐ Subunit 2.3.4: 3 hours

☐ Subunit 2.3.5: 1 hours

☐ Subunit 2.4: 12 hours

☐ Subunit 2.4.1: 2.5 hours

☐ Subunit 2.4.2: 3 hours

☐ Subunit 2.4.3: 2.5 hours

☐ Subunit 2.4.4: 3 hours

☐ Subunit 2.4.5: 1 hour

Unit2 Learning Outcomes
Upon successful completion of this unit, the student will be able to:
- Identify and explain appropriate formulas for the calculation of the
properties of solid bodies including area and mass moments of
inertia; perform those calculations.
- Compute strain and stress, and describe the relationship of stress
and strain for elastic, plastic, and composite bodies.
- Compute and describe the relationship betweenstresses and strains in
bodies subjected to tension and torsion.
- Compute stresses and strains in pressure vessels and composites;
identify and explain material properties for such components.
- Identify, explain, and perform calculations involving the concept of
a stress tensor and the constitutive relationship between strain and
stress.

2.1 Properties of Solids2.1.1 Moments of Inertia: Area
- Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s
“Area Moments of Inertia”
Link: University of Nebraska at Lincoln: Mehrdad Negahban’s “Area
Moments of
Inertia”
(PDF)

Instructions: Please click on the link above and read the entire
article on computation of moments of inertia.

Terms of Use: The linked material above has been reposted by the
kind permission of Dr. Mehrdad Negahban and can be viewed in its
original
form [here](http://emweb.unl.edu/negahban/em223/note18/note18.htm) (HTML). Please
note that this material is under copyright and may not be reproduced
in any capacity without the explicit permission of the copyright
holder.

Instructions: Please click on the link above and read the entire
article. What is the difference between the mass and area moments
of inertia? What is the radius of gyration? Be sure to read the
examples provided.

Terms of Use: This resource has been reposted by the kind
permission of Dr. Mehrdad Negahban and can be viewed in its original
form here (HTML). Please
note that this material is under copyright and may not be reproduced
in any capacity without the explicit permission of the copyright
holder.

Instructions: Please click on the link above and read the entire
article.

Terms of Use: This resource is released under a [Creative Commons
Attribution-Non Commercial-Share-Alike 3.0
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to MIT's [OpenCourseWare](http://ocw.mit.edu/index.htm)
and David Roylance, and the original version can be found
[here](http://ocw.mit.edu/courses/materials-science-and-engineering/3-11-mechanics-of-materials-fall-1999/modules/elas_1.pdf).

Lecture: Elasticity and Young's Modulus
The Saylor Foundation does not yet have materials for this portion
of the course. If you are interested in contributing your content to
fill this gap or aware of a resource that could be used here, please
submit it here.

Instructions: Please click on the link above and read the entire
article. You may wish to peruse the technical data for commercial
devices that accomplish the tests described in the document. This
information can be found with an Internet search for terms such as
“tensile testing.”

Terms of Use: This resource is licensed under a [Creative Commons
Attribution 3.0
License](http://creativecommons.org/licenses/by/3.0/). It is
attributed to The Saylor Foundation.

Instructions: Please click the link above and complete all the
questions. These questions ask for your qualitative and
quantitative understanding of stress and strain. If you have
difficulty, you might benefit most from studying the resources,
especially the example calculations contained therein, for subunit
2.2 again. When you finish, check your answer against The Saylor
Foundation's [“Materials Response Answer
Key”](http://www.saylor.org/site/wp-content/uploads/2012/10/ME1022.2.52.pdf).
Terms of Use: This resource is licensed under a [Creative Commons
Attribution 3.0
License](http://creativecommons.org/licenses/by/3.0/). It is
attributed to The Saylor Foundation.

Instructions: Please click on the link above and complete all the
questions. Please consult resources from subunit 2.3 work on the
activity. After completion, please refer to The Saylor Foundation's
[“Subunit 2.3.5 Review Activity Answer
Key”](http://www.saylor.org/site/wp-content/uploads/2012/09/ME1022.3.52.pdf).
Terms of Use: This resource is licensed under a [Creative Commons
Attribution 3.0
License](http://creativecommons.org/licenses/by/3.0/). It is
attributed to The Saylor Foundation.

Instructions: Please click on the link above and complete all the
questions. Please consult the resources from subunit 2.4 as you
work. After completion, please refer to The Saylor
Foundation's [“Subunit 2.4.5 Review Activity Answer
Key”](http://www.saylor.org/site/wp-content/uploads/2012/09/ME1022.4.52.pdf) (PDF).
Terms of Use: This resource is licensed under a [Creative Commons
Attribution 3.0
License](http://creativecommons.org/licenses/by/3.0/). It is
attributed to The Saylor Foundation.

Intructions: Please click on the link above and complete the
assessment.
You must be logged into your Saylor Foundation School account in
order to access this exam. If you do not yet have an account, you
will be able to create one, free of charge, after clicking the
link.
Terms of Use: This resource is licensed under a [Creative Commons
Attribution 3.0
License](http://creativecommons.org/licenses/by/3.0/). It is
attributed to The Saylor Foundation.